So what are differential equations?
Well, we're used to using algebra to solve for an unknown variable. With differential equations, we use calculus to solve for an unknown function.
A differential equation is any equation that contains the derivative of an unknown function. Sometimes it is not possible to find a solution to the function due to the complexity of the equation. When a differential equation is solvable, this is usually an infinite number of solutions.
In this video, we recap some of the basic mechanics behind differential notation, where df/dx are separable. This is very useful for solving basic differential equations.
We then solve 2 of the simplest forms of differential equation:
f'(x) = 3x2 + 4x + 1
An application of finding the solution to the simplest form of differential equations - We find the solution to the displacement as a function of time of an object with constant acceleration a, initial velocity u, and initial displacement s(0) = 0.
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